Estimation of the l_2-norm and testing in sparse linear regression with unknown variance

10/26/2020

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by   Alexandra Carpentier, et al.

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We consider the related problems of estimating the l_2-norm and the squared l_2-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with l_2 separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.